KILLED proof of input_P3FpHH7hai.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 0 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), 9 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 69 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 25 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 151 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (186) CdtProblem (187) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 31 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (192) CdtProblem (193) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 27 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms] (198) CdtProblem (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 39 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22.2 s] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 16 ms] (206) 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))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0') -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0') -> 0' mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) 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] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (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] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (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__plus_2 a__and_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] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (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] mark(and(and(X111, X211), X2)) -> a__and(a__and(mark(X111), X211), X2) [2] mark(and(plus(X112, X212), X2)) -> a__and(a__plus(mark(X112), mark(X212)), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(and(s(X7), X2)) -> a__and(s(mark(X7)), X2) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (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 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__and(a__plus(mark(X112), mark(X212)), X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X111), X211), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X7), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (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 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__and(a__plus(mark(X112), mark(X212)), X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X111), X211), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X7), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (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] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (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 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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_1, c3_2, c4_2, c5, c6_2, c7_2, c8_2, c9, c10, c11_1 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: A__PLUS(z0, z1) -> c5 A__AND(z0, z1) -> c1 MARK(0) -> c10 MARK(tt) -> c9 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c3_2, c4_2, c6_2, c7_2, c8_2, c11_1 ---------------------------------------- (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(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c6_2, c7_2, c8_2, c11_1, c3_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1 ---------------------------------------- (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(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1 ---------------------------------------- (35) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1 ---------------------------------------- (41) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) by A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) by A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by A__PLUS(and(x0, x1), s(and(z0, z1))) -> c3(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(plus(z0, z1))) -> c3(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(s(z0))) -> c3(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) by A__PLUS(plus(x0, x1), s(and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(s(z0))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by A__PLUS(s(x0), s(and(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) A__PLUS(s(x0), s(plus(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(x0), s(s(z0))) -> c3(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) by A__PLUS(tt, s(and(z0, z1))) -> c3(A__PLUS(tt, a__and(mark(z0), z1))) A__PLUS(tt, s(plus(z0, z1))) -> c3(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(tt, s(s(z0))) -> c3(A__PLUS(tt, s(mark(z0)))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) by A__PLUS(0, s(and(z0, z1))) -> c3(A__PLUS(0, a__and(mark(z0), z1))) A__PLUS(0, s(plus(z0, z1))) -> c3(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(0, s(s(z0))) -> c3(A__PLUS(0, s(mark(z0)))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) by A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by A__PLUS(and(x0, x1), s(and(z0, z1))) -> c4(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(and(x0, x1), s(plus(z0, z1))) -> c4(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, x1), s(s(z0))) -> c4(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (95) 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)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by A__PLUS(plus(x0, x1), s(and(z0, z1))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(plus(x0, x1), s(plus(z0, z1))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(s(z0))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (101) 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)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) by A__PLUS(tt, s(and(z0, z1))) -> c4(A__PLUS(tt, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(tt, s(plus(z0, z1))) -> c4(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) A__PLUS(tt, s(s(z0))) -> c4(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) by A__PLUS(0, s(and(z0, z1))) -> c4(A__PLUS(0, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(0, s(plus(z0, z1))) -> c4(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) A__PLUS(0, s(s(z0))) -> c4(A__PLUS(0, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) by A__PLUS(s(x0), s(and(z0, z1))) -> c4(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(s(x0), s(plus(z0, z1))) -> c4(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(x0), s(s(z0))) -> c4(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) by MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) by MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) by MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) by MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by MARK(plus(and(x0, x1), and(z0, z1))) -> c7(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) MARK(plus(and(x0, x1), plus(z0, z1))) -> c7(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(and(x0, x1))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, x1), s(z0))) -> c7(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) by MARK(plus(plus(x0, x1), and(z0, z1))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), s(z0))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(plus(s(x0), and(z0, z1))) -> c7(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) MARK(plus(s(x0), plus(z0, z1))) -> c7(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(x0), s(z0))) -> c7(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) by MARK(plus(tt, and(z0, z1))) -> c7(A__PLUS(tt, a__and(mark(z0), z1))) MARK(plus(tt, plus(z0, z1))) -> c7(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(tt, s(z0))) -> c7(A__PLUS(tt, s(mark(z0)))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) by MARK(plus(0, and(z0, z1))) -> c7(A__PLUS(0, a__and(mark(z0), z1))) MARK(plus(0, plus(z0, z1))) -> c7(A__PLUS(0, a__plus(mark(z0), mark(z1)))) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(0, s(z0))) -> c7(A__PLUS(0, s(mark(z0)))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) by MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by MARK(plus(and(x0, x1), and(z0, z1))) -> c8(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(and(x0, x1), plus(z0, z1))) -> c8(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, x1), s(z0))) -> c8(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(plus(plus(x0, x1), and(z0, z1))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), s(z0))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) by MARK(plus(tt, and(z0, z1))) -> c8(A__PLUS(tt, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(tt, plus(z0, z1))) -> c8(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) MARK(plus(tt, s(z0))) -> c8(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (187) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) by MARK(plus(0, and(z0, z1))) -> c8(A__PLUS(0, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(0, plus(z0, z1))) -> c8(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) MARK(plus(0, s(z0))) -> c8(A__PLUS(0, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (193) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), 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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(plus(s(x0), and(z0, z1))) -> c8(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(s(x0), plus(z0, z1))) -> c8(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(x0), s(z0))) -> c8(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) by MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), 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) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2